When compared with other summary statistics (mean size, size variance, orientation variance), visual estimates of average orientation are inefficient. Observers act as if they use information from no more than two or three items. We hypothesised that observers would attain greater sampling efficiency when their task did not require an explicit representation of mean orientation. To test this hypothesis, we presented two arrays of 32 Gabor patterns each; one left and one right of fixation. Orientations in the target array were sampled from Wrapped Normal distributions having two different means. One distribution defined orientations above the horizontal meridian, the other defined orientations below the meridian. All orientations in the other array were defined by a single Wrapped Normal distribution having the same variance. Contrary to our hypothesis, model fits indicate that observers effectively ignored all but one item from the top and bottom of each array. In fact, we found no change in the threshold difference between the target's two means when all but one item from the top and bottom of each array were removed. We are forced to conclude that the visual system does not compute the average of more than a few orientations, even for texture segmentation.